Nonlocal dynamic temperature stress simulation

Abstract

Abstract The development of technologies for obtaining consolidated structural materials has increased interest in modelling materials with a heterogeneous structure. For models of such materials, an important factor is the relationship between the characteristics of the micro-(nano- ) level and the laws of continuum mechanics at the macro level. The widespread use of modern structure-sensitive materials in extreme conditions is the reason for the urgency of the problem of developing methods of mathematical modelling that allow describing such materials. New nonlinear dynamic problems that arise in this case require a new approach to the study and prediction of the mechanical behavior of such materials under conditions of high-intensity external influences. The paper considers a nonlocal model of dynamic temperature stresses. The model is based on the methods of globalized continuum mechanics. The basic equations of the model are derived from conservation laws. The model of thermomechanical processes in a nonlocal medium includes integro-differential equations with various boundary conditions. Equations describe stress in structural members. Also, the paper proposes an algorithm based on the finite element method to solve the problem. The distributions of temperature stresses in the nonlocal layer of the material are obtained and the influence of the main parameters of nonlocality on the solution of the problem is analyzed.